Differential Geometry in Neural Implicits

• DOI: 10.2139/ssrn.4109687
• Publication Date: 2022-05-28T12:08:19Z
• Authors: Tiago Novello; Vinicius da Silva; Guilherme Schardong; Luiz Schirmer; HELIO LOPES; Luiz Velho
• Keywords: 0202 electrical engineering, electronic engineering, information engineering; 02 engineering and technology

We introduce a neural implicit framework that bridges discrete differential geometry of triangle meshes and continuous surfaces. It exploits the differentiable properties networks to approximate them as level sets functions . To train function, we propose loss functional allows terms with high-order derivatives, such alignment between principal directions curvature, learn more geometric details. During training, consider non-uniform sampling strategy based on curvatures mesh access points This implies faster learning while preserving accuracy. also present analytical formulas for surfaces, normal vectors curvatures.